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Search: id:A148158
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| A148158 |
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Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, 0, 1), (0, -1, 1), (0, 1, 0), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 4, 11, 30, 99, 321, 1125, 3994, 14669, 54883, 210009, 816899, 3221481, 12875307, 51984975, 211956185, 871637092, 3613651770, 15086421954, 63391684221, 267934026055, 1138417265769, 4860596083277, 20847396593292, 89793624085992, 388259714531135, 1684888139692659, 7336277575618726
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A148157 A141268 A135527 this_sequence A148159 A102814 A034770
Adjacent sequences: A148155 A148156 A148157 this_sequence A148159 A148160 A148161
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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